{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter XX\n",
    "\n",
    "# XXXX\n",
    "Book_3《数学要素》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5973a20e-6bbe-4332-a53b-bbd6794ecced",
   "metadata": {},
   "source": [
    "这段代码的目的是通过泰勒展开的二次近似来研究函数\n",
    "\n",
    "$$\n",
    "f(x) = e^{-x^2}\n",
    "$$\n",
    "\n",
    "及其一阶导数在不同点附近的变化趋势。具体来说，代码分两个部分进行分析：首先对函数 $f(x)$ 进行二次近似，然后对其一阶导数 $\\frac{df}{dx}$ 进行二次近似。二次近似即在某一中心点 $x_0$ 处用泰勒展开式的前几项来逼近函数。\n",
    "\n",
    "1. **对 $f(x)$ 的二次近似**：\n",
    "   对于给定的中心点 $x_0$，在 $f(x)$ 的泰勒展开式中，使用一阶和二阶导数的信息来构建二次多项式近似。该近似表达式为：\n",
    "\n",
    "   $$\n",
    "   f(x) \\approx f(x_0) + f'(x_0)(x - x_0) + \\frac{f''(x_0)}{2}(x - x_0)^2\n",
    "   $$\n",
    "\n",
    "   其中 $f(x_0)$ 是 $f(x)$ 在 $x_0$ 处的值，$f'(x_0)$ 是一阶导数在该点的值，$f''(x_0)$ 是二阶导数在该点的值。通过在多个 $x_0$ 上进行该近似，生成了不同位置的局部二次近似图，从而直观展示 $f(x)$ 在不同点的变化趋势。\n",
    "\n",
    "2. **对 $\\frac{df}{dx}$ 的二次近似**：\n",
    "   对 $f(x)$ 的一阶导数 $\\frac{df}{dx}$，也在多个 $x_0$ 点处进行二次近似。类似地，构建了以下二次多项式：\n",
    "\n",
    "   $$\n",
    "   f'(x) \\approx f'(x_0) + f''(x_0)(x - x_0) + \\frac{f'''(x_0)}{2}(x - x_0)^2\n",
    "   $$\n",
    "\n",
    "   其中 $f'(x_0)$ 是 $\\frac{df}{dx}$ 在 $x_0$ 处的值，$f''(x_0)$ 是二阶导数在该点的值，$f'''(x_0)$ 是三阶导数在该点的值。这样可以得到 $\\frac{df}{dx}$ 的局部二次近似曲线，展示导数的变化情况。\n",
    "\n",
    "通过对 $f(x)$ 及其一阶导数在不同位置的二次近似，代码揭示了函数的局部行为和趋势。近似曲线的绘制展示了 $f(x)$ 和 $\\frac{df}{dx}$ 的不同光滑性、对称性和变化速度，有助于理解函数在不同点的局部特性。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb032505-1f70-49e7-83ed-8af6d437d080",
   "metadata": {},
   "source": [
    "## 导入包"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f091ae74-03b7-474f-a838-4fd552f42734",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import lambdify, diff, evalf, sin, exp  # 导入必要的符号库函数\n",
    "from sympy.abc import x  # 导入符号变量x\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt  # 导入Matplotlib用于绘图\n",
    "from matplotlib import cm  # 导入colormap模块"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38db8c94-3659-41a2-b315-df94a5aacd02",
   "metadata": {},
   "source": [
    "## 定义函数f(x) = exp(-x^2)并计算其值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "145f27ec-998d-45fb-9e6c-238fffaff598",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e^{- x^{2}}$"
      ],
      "text/plain": [
       "exp(-x**2)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_x = exp(-x**2)  # 定义函数f(x)为exp(-x^2)\n",
    "f_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "96364d43-a924-439e-8712-7d63dd5e7385",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_array = np.linspace(-3, 3, 100)  # 定义x的取值范围，用于绘制函数曲线\n",
    "x_0_array = np.linspace(-2.5, 2.5, 21)  # 定义用于展开的中心点x_0的范围"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b200e698-5e66-4c2f-82b0-73f37df3eca3",
   "metadata": {},
   "outputs": [],
   "source": [
    "f_x_fcn = lambdify(x, f_x)  # 将符号函数f(x)转换为可数值计算的函数\n",
    "f_x_array = f_x_fcn(x_array)  # 计算f(x)在x_array上的值"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "682c08b0-d1bf-40cc-8fcd-602df29b4354",
   "metadata": {},
   "source": [
    "## 绘制函数f(x)的二次近似"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4a282009-4440-448c-8dfb-f83871056cdd",
   "metadata": {},
   "outputs": [],
   "source": [
    "colors = plt.cm.rainbow(np.linspace(0, 1, len(x_0_array)))  # 使用彩虹颜色映射，生成每个x_0的颜色"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "298a8f3e-cf08-4378-80fa-78b7350c4885",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 2 x e^{- x^{2}}$"
      ],
      "text/plain": [
       "-2*x*exp(-x**2)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_x_1_diff = diff(f_x, x)  # 计算f(x)的一阶导数\n",
    "f_x_1_diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e64d1f57-f260-4d3b-b29e-0c7372ba0c07",
   "metadata": {},
   "outputs": [],
   "source": [
    "f_x_1_diff_fcn = lambdify(x, f_x_1_diff)  # 将一阶导数转化为可数值计算的函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f342ab74-4252-44e9-ad88-318856b3b5af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 \\left(2 x^{2} - 1\\right) e^{- x^{2}}$"
      ],
      "text/plain": [
       "2*(2*x**2 - 1)*exp(-x**2)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_x_2_diff = diff(f_x, x, 2)  # 计算f(x)的二阶导数\n",
    "f_x_2_diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c05e19dd-afaf-4b9e-a639-7bac0c0d954f",
   "metadata": {},
   "outputs": [],
   "source": [
    "f_x_2_diff_fcn = lambdify(x, f_x_2_diff)  # 将二阶导数转化为可数值计算的函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e678ca0b-9e08-4d46-b47c-b8a59b5ddbe3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.25, 1.25)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()  # 创建绘图窗口\n",
    "\n",
    "ax.plot(x_array, f_x_array, linewidth=1.5)  # 绘制原函数f(x)曲线\n",
    "ax.set_xlabel(r\"$\\it{x}$\")  # 设置x轴标签\n",
    "ax.set_ylabel(r\"$\\it{f}(\\it{x})$\")  # 设置y轴标签\n",
    "\n",
    "for i in np.arange(len(x_0_array)):\n",
    "    color = colors[i, :]  # 选择颜色\n",
    "    x_0 = x_0_array[i]  # 获取当前的x_0值\n",
    "    y_0 = f_x.evalf(subs={x: x_0})  # 计算f(x_0)\n",
    "    x_t_array = np.linspace(x_0 - 0.5, x_0 + 0.5, 50)  # 定义近似区间的x取值范围\n",
    "\n",
    "    b = f_x_1_diff.evalf(subs={x: x_0})  # 计算一阶导数在x_0的值\n",
    "    a = f_x_2_diff.evalf(subs={x: x_0})  # 计算二阶导数在x_0的值\n",
    "\n",
    "    second_order_f = a/2 * (x - x_0)**2 + b * (x - x_0) + y_0  # 构建二次近似多项式\n",
    "    second_order_f_fcn = lambdify(x, second_order_f)  # 将二次近似多项式转换为数值函数\n",
    "    second_order_f_array = second_order_f_fcn(x_t_array)  # 计算近似曲线在x_t_array上的值\n",
    "\n",
    "    ax.plot(x_t_array, second_order_f_array, linewidth=0.25, color=color)  # 绘制近似曲线\n",
    "    ax.plot(x_0, y_0, marker='.', color=color, markersize=12)  # 标记近似中心点\n",
    "\n",
    "ax.grid(linestyle='--', linewidth=0.25, color=[0.5, 0.5, 0.5])  # 添加网格\n",
    "ax.set_xlim((x_array.min(), x_array.max()))  # 设置x轴范围\n",
    "ax.set_ylim(-0.25, 1.25)  # 设置y轴范围"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b6246bf-a91b-4535-ad42-393f57d8d994",
   "metadata": {},
   "source": [
    "## 在每个x_0点处绘制二次近似曲线"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9436d0d5-a697-4a17-9159-dec1c3ece13c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "a7964e2f-1279-4e71-847c-c4e99c3c0b71",
   "metadata": {},
   "source": [
    "## 绘制一阶导数的二次近似"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c60eb52e-0e71-45d0-827f-e73427796f78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 2 x e^{- x^{2}}$"
      ],
      "text/plain": [
       "-2*x*exp(-x**2)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_x_1_diff_new = diff(f_x, x)  # 重新计算f(x)的一阶导数\n",
    "f_x_1_diff_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "90ac2fd0-9ff7-453f-b8f5-98cf2960fadd",
   "metadata": {},
   "outputs": [],
   "source": [
    "f_x_1_diff_fcn_new = lambdify(x, f_x_1_diff_new)  # 转换为可数值计算的函数\n",
    "f_x_1_diff_array_new = f_x_1_diff_fcn_new(x_array)  # 计算一阶导数在x_array上的值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "af801d64-4600-41cb-a1dc-09b30882f355",
   "metadata": {},
   "outputs": [],
   "source": [
    "colors = plt.cm.rainbow(np.linspace(0, 1, len(x_0_array)))  # 使用彩虹色映射"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1e882597-20bd-43e6-a3f2-02e41c8393b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 \\left(2 x^{2} - 1\\right) e^{- x^{2}}$"
      ],
      "text/plain": [
       "2*(2*x**2 - 1)*exp(-x**2)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_x_1_diff = diff(f_x, x, 2)  # 计算二阶导数\n",
    "f_x_1_diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "02609171-f987-47ee-b302-4512b19a2a49",
   "metadata": {},
   "outputs": [],
   "source": [
    "f_x_1_diff_fcn = lambdify(x, f_x_1_diff)  # 转换为可数值计算的函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "61dc7a9c-1fa3-43cd-9b47-1fd6e88aa3bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 4 x \\left(3 - 2 x^{2}\\right) e^{- x^{2}}$"
      ],
      "text/plain": [
       "4*x*(3 - 2*x**2)*exp(-x**2)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_x_2_diff = diff(f_x, x, 3)  # 计算三阶导数\n",
    "f_x_2_diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "fa0943ce-3197-4cea-a922-6ce7f81863fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "f_x_2_diff_fcn = lambdify(x, f_x_2_diff)  # 转换为可数值计算的函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "50b1643a-a9ff-4d78-b7b9-21fe011be991",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.25, 1.25)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()  # 创建新图\n",
    "\n",
    "ax.plot(x_array, f_x_1_diff_array_new, linewidth=1.5)  # 绘制一阶导数曲线\n",
    "ax.set_xlabel(r\"$\\it{x}$\")  # 设置x轴标签\n",
    "ax.set_ylabel(r\"$\\it{f}(\\it{x})$\")  # 设置y轴标签\n",
    "\n",
    "for i in np.arange(len(x_0_array)):\n",
    "    color = colors[i, :]  # 选择颜色\n",
    "    x_0 = x_0_array[i]  # 获取当前的x_0值\n",
    "    y_0 = f_x_1_diff_new.evalf(subs={x: x_0})  # 计算一阶导数在x_0的值\n",
    "    x_t_array = np.linspace(x_0 - 0.5, x_0 + 0.5, 50)  # 定义近似区间的x取值范围\n",
    "\n",
    "    b = f_x_1_diff.evalf(subs={x: x_0})  # 计算二阶导数在x_0的值\n",
    "    a = f_x_2_diff.evalf(subs={x: x_0})  # 计算三阶导数在x_0的值\n",
    "\n",
    "    second_order_f = a/2 * (x - x_0)**2 + b * (x - x_0) + y_0  # 构建一阶导数的二次近似多项式\n",
    "    second_order_f_fcn = lambdify(x, second_order_f)  # 转换为数值函数\n",
    "    second_order_f_array = second_order_f_fcn(x_t_array)  # 计算近似曲线的值\n",
    "\n",
    "    ax.plot(x_t_array, second_order_f_array, linewidth=0.25, color=color)  # 绘制近似曲线\n",
    "    ax.plot(x_0, y_0, marker='.', color=color, markersize=12)  # 标记近似中心点\n",
    "\n",
    "ax.grid(linestyle='--', linewidth=0.25, color=[0.5, 0.5, 0.5])  # 添加网格\n",
    "ax.set_xlim((x_array.min(), x_array.max()))  # 设置x轴范围\n",
    "ax.set_ylim(-1.25, 1.25)  # 设置y轴范围"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "62206bda-2cc9-441d-8d76-ed56a901ecc2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
